Answer to Question #300213 in Mechanical Engineering for king

Question

In a Diesel engine inlet pressure and temperature are 1 bar and 17 oC respectively. Pressure at the end of adiabatic compression is 35 bar. The ratio of expansion i.e. after constant pressure heat addition is 5. Calculate the heat addition, heat rejection and the efficiency of the cycle. Assume Cv = 0.717 kJ/ kg K, 𝛾=1.4 

Answer 1

$P_1 = 1$ $T_1 =17=290^0K$ $P_2= 32$ bar

$\frac{P_2}{P_1}= \frac{T_2}{T_1}^{\frac{k}{k-1}}$

$T_2 = T_1(\frac{P_2}{P_1})^{\frac{k-1}{k}}$

$T_2=290\times \frac{32}{1}^{0.2857} =780.58^0K$

$P_4 = \frac{P_2}{5}=\frac{32}{5}=6.4$ bar

$T_4 = T_1(\frac{P_4}{P_1})^{\frac{k-1}{k}}$

$T_4=290\times \frac{6.4}{1}^{0.2857} =483.85^0K$

Heat addition:

$Q_{in}= m C_v\triangle T= 1\times 0.717\times(T_2-T_1)=1\times 0.717\times(780.58-290)=351.74 \frac{kJ}{kg K}$

Heat rejection :

$Q_{out}= m C_v\triangle T= 1\times 0.717\times(T_4-T_1)=1\times 0.717\times(483.85-290)=193.85\frac{kJ}{kg K}$

Efficiency of the cycle:

$\eta_{th}= \frac{Q_{in}-Q_{out}}{Q_{in}}= \frac{351.74-193.85}{351.74}=0.4488=45$%